Due:

$10/30/24$

The concept layout is shown for a geared industrial roll driven at $300$ rpm by a force $\backslash ($ F $\backslash )($at $\backslash (20^\{\backslash$circ$\}\backslash )$ off the horizontal line$)$ acting on a gear with $3-$inch$-$diameter pitch circle $($at B $).$ All dimensions are in inch.

The roll exerts a normal force of $\backslash (40\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$in$\}\backslash )$ of roll length on the materials being pulled through and under the roll due to frictions. The coefficient of friction between the roll and the material is $0\mathrm{.}40.$ The outside diameter of the roll is $4$ inches whereas the inner diameter is unset but cannot exceed $1\mathrm{.}75$ inches. The roll should not have any axial movement during operations.

Design a shaft for the situation of the industrial roll with a design factor of $2$ and a reliability factor of $\backslash (99\mathrm{.}9\backslash \%\backslash )$ against fatigue failure. The shaft support plan is to use ball bearings on the left at O and on the right at A$.$ Shaft deformation characterization at bearings is not required but is left as bonus task in this project. For shaft deformation use a factor of safety of $2.$